{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lagrangian Neural Networks\n",
    "\n",
    "In this tutorial we take a look at **Lagrangian Nets** (LNNs) first proposed in [Lutter M., et al, 2019](https://arxiv.org/abs/1907.04490) and generalized by [Cranmer M., et al., 2020](https://arxiv.org/abs/2003.04630). Together with HNNs [Greydanus S., et al., 2019](https://arxiv.org/abs/1906.01563), LNNs represent the latest learning paradigm to discover symmetries and conservation laws from data.\n",
    "\n",
    "Let $\\mathcal{Q}\\subset\\mathbb{R}^n$ be a smooth manifold anf let $q\\in\\mathcal{Q}$ be a vector of generalized coordinates. The Lagrangian function $\\mathcal{L}:\\mathcal{TQ}\\rightarrow\\mathbb{R}$ is defined on the tangent bundle $\\mathcal{TQ}$ of the configuration manifold $\\mathcal{Q}$ (if $\\mathcal{Q}=\\mathbb{R}^n$, then $\\mathcal{TQ}$ is diffeomorphic to $\\mathbb{R}^{2n}$), i.e. the Lagrangian is a function of the configurations $q$ and their velocities $\\dot q$.\n",
    "\n",
    "Derived from the calculus of variations, the Euler-Lagrange equations of motions can be generally explicitly written as a second-order ordinary differential equation:\n",
    "\n",
    "$$\n",
    "    \\ddot q = \\left(\\nabla_{\\dot q} \\nabla_{\\dot q}^\\top \\mathcal{L}\\right)^{-1}\\left[\\nabla_q\\mathcal{L} - \\left(\\nabla_q\\nabla^\\top_{\\dot q}\\mathcal L\\right)\\dot q\\right]\n",
    "$$\n",
    "\n",
    "**Lagrangian Neural Networks** try to mimick Euler-Lagrange equations by learning from data a Lagrangian $\\mathcal{L}_\\theta$ parametriezed by a *neural network* (with parameters $\\theta$). \n",
    "\n",
    "When a net of tuples $\\{(q_k,\\dot q_k, \\ddot q_k)\\}_{k=1,\\dots,K}$ generated by some conservative dynamical process is available, LNNs are trained to learn the Lagrangian from the data by minimizing, e.g. the *MSE loss*:\n",
    "$$\n",
    "    \\min_{\\theta}\\frac{1}{K}\\sum_{k=1}^K\\left\\|\\ddot q_k - \\left(\\nabla_{\\dot q} \\nabla_{\\dot q}^\\top \\mathcal{L}_\\theta(q_k, \\dot q_k)\\right)^{-1}\\left[\\nabla_q\\mathcal{L}_\\theta(q_k, \\dot q_k) - \\left(\\nabla_q\\nabla^\\top_{\\dot q}\\mathcal L_\\theta(q_k, \\dot q_k)\\right)\\dot q_k\\right]\\right\\|_2^2\n",
    "$$\n",
    "\n",
    "\n",
    "We hereby showcase the torchdyn implementation of LNNs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torchdyn.models import *; from torchdyn.datasets import *\n",
    "from torchdyn import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vector field of an LNN, to be passed to a `NeuralDE` can be defined as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.autograd import grad\n",
    "\n",
    "class LNN(nn.Module):\n",
    "    def __init__(self, L):\n",
    "        super().__init__()   \n",
    "        self.L = L   \n",
    "    def forward(self, x):\n",
    "        with torch.set_grad_enabled(True):\n",
    "            self.n = n = x.shape[1]//2 \n",
    "            qqd = x.requires_grad_(True)\n",
    "            L = self._lagrangian(qqd).sum()\n",
    "            J = grad(L, qqd, create_graph=True)[0] ;\n",
    "            DL_q, DL_qd = J[:,:n], J[:,n:]\n",
    "            DDL_qd = []\n",
    "            for i in range(n):\n",
    "                J_qd_i = DL_qd[:,i][:,None]\n",
    "                H_i = grad(J_qd_i.sum(), qqd, create_graph=True)[0][:,:,None]\n",
    "                DDL_qd.append(H_i)\n",
    "            DDL_qd = torch.cat(DDL_qd, 2)\n",
    "            DDL_qqd, DDL_qdqd = DDL_qd[:,:n,:], DDL_qd[:,n:,:]\n",
    "            T = torch.einsum('ijk, ij -> ik', DDL_qqd, qqd[:,n:])\n",
    "            qdd = torch.einsum('ijk, ij -> ik', DDL_qdqd.inverse(), DL_q - T)\n",
    "        return torch.cat([qqd[:,self.n:], qdd], 1)\n",
    "    def _lagrangian(self, qqd):\n",
    "        return self.L(qqd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider a 1D mass-spring system\n",
    "\n",
    "$$\n",
    "    m\\ddot x + kx = 0,~~~[x(0),\\dot x(0)]\\sim \\mathcal N(0,I)\n",
    "$$\n",
    "\n",
    "Following the LNN paper from Cranmer et al., we generate random values of $x,\\dot x$ and we fit (in a static manner) the corresponding $\\ddot q$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"Static\" Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "m, k, l = 1, 1, 1\n",
    "X = torch.Tensor(2**14, 2).uniform_(-1, 1).to(device)\n",
    "Xdd = -k*X[:,0]/m\n",
    "\n",
    "train = data.TensorDataset(X, Xdd)\n",
    "trainloader = data.DataLoader(train, batch_size=64, shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model.defunc(0, x)\n",
    "    \n",
    "    def loss(self, y_hat, y):\n",
    "        return ((y - y_hat[:,1])**2).mean()\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch\n",
    "        y_hat = self.model.defunc(0, x) #static training: we do not solve the ODE \n",
    "        loss = self.loss(y_hat, y)\n",
    "        return {'loss': loss}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.1)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "hdim = 128\n",
    "net = LNN(nn.Sequential(\n",
    "            nn.Linear(2,hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim,hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim,1))\n",
    "         ).to(device)\n",
    "\n",
    "model = NeuralDE(func=net, solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 17 K  \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "64d35333d90346e5875b6ce55ef2581b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(max_epochs=10)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NFE: 20\n",
      "inference time: 0.21263456344604492\n",
      "avg time per function evaluation: 0.010631728172302245\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the training results\n",
    "import time\n",
    "t = time.time()\n",
    "model.nfe = 0\n",
    "X0 = torch.Tensor(256, 2).uniform_(-1,1).to(device)\n",
    "s_span = torch.linspace(0, 1, 100)\n",
    "traj = model.trajectory(X0, s_span).cpu().detach()\n",
    "T = time.time() - t\n",
    "print(f\"NFE: {model.nfe}\\ninference time: {T}\\navg time per function evaluation: {T/model.nfe}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, \"LNN's learned trajectories\")"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the LNN's trajectories with random ICs\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "color = ['orange', 'blue']\n",
    "for i in range(len(X0)):\n",
    "    ax.plot(traj[:,i,0], traj[:,i,1], color='blue', alpha=0.1);\n",
    "ax.set_xlim([-1,1])\n",
    "ax.set_ylim([-1,1])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"LNN's learned trajectories\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Learned Lagrangian & Vector Field')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Lagrangian and learned vector field\n",
    "n_grid =  50 ; x = torch.linspace(-1, 1, n_grid)\n",
    "Q, Qd = torch.meshgrid(x, x); qqd = torch.cat([Q.reshape(-1,1), Qd.reshape(-1,1)], 1).to(device)\n",
    "L = model.defunc.m.L(qqd).detach().cpu().reshape(n_grid, n_grid)\n",
    "UV = model.defunc(0, qqd).detach().cpu() \n",
    "U = UV[:,0].reshape(n_grid, n_grid) ; V = UV[:,1].reshape(n_grid, n_grid)\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.contourf(Q, Qd, L,100,cmap='RdYlBu')\n",
    "ax.streamplot(Q.T.numpy(),Qd.T.numpy(),U.T.numpy(),V.T.numpy(), color='black')\n",
    "ax.set_xlim([Q.min(),Q.max()])\n",
    "ax.set_ylim([Qd.min(),Qd.max()])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$\\dot q$\")\n",
    "ax.set_title(\"Learned Lagrangian & Vector Field\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forced Lagrangian Models\n",
    "\n",
    "Can we easily extend the framework to the non-conservative case where some forcing term is present?\n",
    "\n",
    "Yes of course!\n",
    "\n",
    "We can add a learnable forcinf term $f(q,\\dot q)$ to the system obtaining:\n",
    "\n",
    "$$\n",
    "    \\ddot q = \\left(\\nabla_{\\dot q} \\nabla_{\\dot q}^\\top \\mathcal{L}\\right)^{-1}\\left[\\nabla_q\\mathcal{L} - \\left(\\nabla_q\\nabla^\\top_{\\dot q}\\mathcal L\\right)\\dot q + f(q, \\dot q)\\right]\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class fLNN(nn.Module):\n",
    "    def __init__(self, L, f):\n",
    "        super().__init__()   \n",
    "        self.L, self.f = L, f\n",
    "    def forward(self, x):\n",
    "        with torch.set_grad_enabled(True):\n",
    "            self.n = n = x.shape[1]//2 \n",
    "            qqd = x.requires_grad_(True)\n",
    "            L = self._lagrangian(qqd).sum()\n",
    "            J = grad(L, qqd, create_graph=True)[0] ;\n",
    "            DL_q, DL_qd = J[:,:n], J[:,n:]\n",
    "            DDL_qd = []\n",
    "            for i in range(n):\n",
    "                J_qd_i = DL_qd[:,i][:,None]\n",
    "                H_i = grad(J_qd_i.sum(), qqd, create_graph=True)[0][:,:,None]\n",
    "                DDL_qd.append(H_i)\n",
    "            DDL_qd = torch.cat(DDL_qd, 2)\n",
    "            DDL_qqd, DDL_qdqd = DDL_qd[:,:n,:], DDL_qd[:,n:,:]\n",
    "            T = torch.einsum('ijk, ij -> ik', DDL_qqd, qqd[:,n:])\n",
    "            qdd = torch.einsum('ijk, ij -> ik', DDL_qdqd.inverse(), DL_q - T - self.f(qqd))\n",
    "        return torch.cat([qqd[:,self.n:], qdd], 1)\n",
    "    \n",
    "    def _lagrangian(self, qqd):\n",
    "        return self.L(qqd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now consider, e.g., a 1D mass-spring-damper system \n",
    "\n",
    "$$\n",
    "    m\\ddot x + kx + b\\dot x = 0,~~~[x(0),\\dot x(0)]\\sim \\mathcal N(0,I)\n",
    "$$\n",
    "\n",
    "and we let $q=x$, $p=\\dot x$. We then train the neural network on random generated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "m, k, b = 1, 1, 1\n",
    "X = torch.Tensor(2**15, 2).uniform_(-1, 1).to(device)\n",
    "Xdd = -k*X[:,0]/m - b*X[:,1]/m\n",
    "train = data.TensorDataset(X, Xdd)\n",
    "trainloader = data.DataLoader(train, batch_size=128, shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model.defunc(0, x)\n",
    "    \n",
    "    def loss(self, y_hat, y):\n",
    "        return ((y - y_hat[:,1])**2).mean()\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch\n",
    "        y_hat = self.model.defunc(0, x)\n",
    "        loss = self.loss(y_hat, y)\n",
    "        return {'loss': loss}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "hdim = 128\n",
    "L = nn.Sequential(\n",
    "            nn.Linear(2, hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim, hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim, 1)).to(device)\n",
    "\n",
    "f = nn.Sequential(\n",
    "            nn.Linear(2, hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim, 1)).to(device)\n",
    "net = fLNN(L, f)\n",
    "model = NeuralDE(func=net, solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 17 K  \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3b479b6cd7d544a39aa30dcdfea17b3e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(max_epochs=10)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NFE: 20\n",
      "inference time: 0.1333456039428711\n",
      "avg time per function evaluation: 0.006667280197143554\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the training results\n",
    "import time\n",
    "t = time.time()\n",
    "model.nfe = 0\n",
    "X0 = torch.Tensor(64, 2).uniform_(-1,1).to(device)\n",
    "s_span = torch.linspace(0, 1, 20)\n",
    "traj = model.trajectory(X0, s_span).cpu().detach()\n",
    "T = time.time() - t\n",
    "print(f\"NFE: {model.nfe}\\ninference time: {T}\\navg time per function evaluation: {T/model.nfe}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, \"LNN's learned trajectories\")"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the forced LNN's trajectories with random ICs\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "color = ['orange', 'blue']\n",
    "for i in range(len(X0)):\n",
    "    ax.plot(traj[:,i,0], traj[:,i,1], color='blue', alpha=0.1);\n",
    "ax.set_xlim([-1,1])\n",
    "ax.set_ylim([-1,1])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"LNN's learned trajectories\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Learned Lagrangian & Vector Field')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Lagrangian and learned vector field\n",
    "n_grid =  50 ; x = torch.linspace(-1, 1, n_grid)\n",
    "Q, Qd = torch.meshgrid(x, x); qqd = torch.cat([Q.reshape(-1,1), Qd.reshape(-1,1)], 1).to(device)\n",
    "L = model.defunc.m.L(qqd).detach().cpu().reshape(n_grid, n_grid)\n",
    "UV = model.defunc(0, qqd).detach().cpu() \n",
    "U = UV[:,0].reshape(n_grid, n_grid) ; V = UV[:,1].reshape(n_grid, n_grid)\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.contourf(Q, Qd, L,100,cmap='RdYlBu')\n",
    "ax.streamplot(Q.T.numpy(),Qd.T.numpy(),U.T.numpy(),V.T.numpy(), color='black')\n",
    "ax.set_xlim([Q.min(),Q.max()])\n",
    "ax.set_ylim([Qd.min(),Qd.max()])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$\\dot q$\")\n",
    "ax.set_title(\"Learned Lagrangian & Vector Field\")"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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